Binding free energy analysis of protein-protein docking model structures by evERdock

Assessment of Protein-Protein Docking Models Using Deep Learning

Protein-protein interactions are involved in almost all processes in a living cell and determine the biological functions of proteins. To obtain mechanistic understandings of protein-protein interactions, the tertiary structures of protein complexes have been determined by biophysical experimental methods, such as X-ray crystallography and cryogenic electron microscopy. However, as experimental methods are costly in resources, many computational methods have been developed that model protein complex structures. One of the difficulties in computational protein complex modeling (protein docking) is to select the most accurate models among many models that are usually generated by a docking method. This article reviews advances in protein docking model assessment methods, focusing on recent developments that apply deep learning to several network architectures.

Computed Protein-Protein Enthalpy Signatures as a Tool for Identifying Conformation Sampling Problems

Understanding the thermodynamic signature of protein-peptide binding events is a major challenge in computational chemistry. The complexity generated by both components possessing many degrees of freedom poses a significant issue for methods that attempt to directly compute the enthalpic contribution to binding. Indeed, the prevailing assumption has been that the errors associated with such approaches would be too large for them to be meaningful. Nevertheless, we currently have no indication of how well the present methods would perform in terms of predicting the enthalpy of binding for protein-peptide complexes. To that end, we carefully assembled and curated a set of 11 protein-peptide complexes where there is structural and isothermal titration calorimetry data available and then computed the absolute enthalpy of binding. The initial "out of the box" calculations were, as expected, very modest in terms of agreement with the experiment. However, careful inspection of the outliers allows for the identification of key sampling problems such as distinct conformations of peptide termini not being sampled or suboptimal cofactor parameters. Additional simulations guided by these aspects can lead to a respectable correlation with isothermal titration calorimetry (ITC) experiments (R2 of 0.88 and an RMSE of 1.48 kcal/mol overall). Although one cannot know prospectively whether computed ITC values will be correct or not, this work shows that if experimental ITC data are available, then this in conjunction with computed ITC, can be used as a tool to know if the ensemble being simulated is representative of the true ensemble or not. That is important for allowing the correct interpretation of the detailed dynamics of the system with respect to the measured enthalpy. The results also suggest that computational calorimetry is becoming increasingly feasible. We provide the data set as a resource for the community, which could be used as a benchmark to help further progress in this area.

Prediction of Protein-Protein Binding Affinities from Unbound Protein Structures

Proteins are the workhorses of cells to carry out sophisticated and complex cellular processes. Such processes require a coordinated and regulated interactions between proteins that are both time and location specific. The strength, or binding affinity, of protein-protein interactions ranges between the micro- and the nanomolar association constant, often dictating the molecular mechanisms underlying the interaction and the longevity of the complex, i.e., transient or permanent. In consequence, there is a need to quantify the strength of protein-protein interactions for biological, biomedical, and biotechnological applications. While experimental methods are labor intensive and costly, computational ones are useful tools to predict the affinity of protein-protein interactions. In this chapter, we review the methods developed by us to address this question. We briefly present two methods to comprehend the structure of the protein complex derived by either comparative modeling or docking. Then we introduce BADOCK, a method to predict the binding energy without requiring the structure of the protein complex, thus overcoming one of the major limitations of structure-based methods for the prediction of binding affinity. BADOCK utilizes the structure of unbound proteins and the protein docking sampling space to predict protein-protein binding affinities. We present step-by-step protocols to utilize these methods, describing the inputs and potential pitfalls as well as their respective strengths and limitations.

Solvation energetics of proteins and their aggregates analyzed by all-atom molecular dynamics simulations and the energy-representation theory of solvation

Solvation is a controlling factor for the structure and function of proteins. This article addresses the effects of solvation from an energetic perspective for the fluctuations and cosolvent-induced changes in protein structures and the equilibrium of aggregate formation for a peptide. A theoretical framework to analyze the solvation effects with an explicit solvent is introduced by adopting the energy-representation theory of solvation, and the connection of the solvation free energy to the protein structure and the aggregation tendency is quantitatively described in combination with all-atom molecular dynamics simulations. The interaction components that govern the solvation effects on the structural variations of proteins are further identified through correlation analysis, and a computational scheme to assess the shift of an aggregation equilibrium due to the addition of a cosolvent is provided.

Native or Non-Native Protein-Protein Docking Models? Molecular Dynamics to the Rescue

Molecular docking excels at creating a plethora of potential models of protein-protein complexes. To correctly distinguish the favorable, native-like models from the remaining ones remains, however, a challenge. We assessed here if a protocol based on molecular dynamics (MD) simulations would allow distinguishing native from non-native models to complement scoring functions used in docking. To this end, the first models for 25 protein-protein complexes were generated using HADDOCK. Next, MD simulations complemented with machine learning were used to discriminate between native and non-native complexes based on a combination of metrics reporting on the stability of the initial models. Native models showed higher stability in almost all measured properties, including the key ones used for scoring in the Critical Assessment of PRedicted Interaction (CAPRI) competition, namely the positional root mean square deviations and fraction of native contacts from the initial docked model. A random forest classifier was trained, reaching a 0.85 accuracy in correctly distinguishing native from non-native complexes. Reasonably modest simulation lengths of the order of 50-100 ns are sufficient to reach this accuracy, which makes this approach applicable in practice.

Prediction of protein-protein complexes using replica exchange with repulsive scaling

The realistic prediction of protein-protein complex structures is import to ultimately model the interaction of all proteins in a cell and for the design of new protein-protein interactions. In principle, molecular dynamics (MD) simulations allow one to follow the association process under realistic conditions including full partner flexibility and surrounding solvent. However, due to the many local binding energy minima at the surface of protein partners, MD simulations are frequently trapped for long times in transient association states. We have designed a replica-exchange based scheme employing different levels of a repulsive biasing between partners in each replica simulation. The bias acts only on intermolecular interactions based on an increase in effective pairwise van der Waals radii (repulsive scaling (RS)-REMD) without affecting interactions within each protein or with the solvent. For a set of five protein test cases (out of six) the RS-REMD technique allowed the sampling of near-native complex structures even when starting from the opposide site with respect to the native binding site for one partner. Using the same start structures and same computational demand regular MD simulations sampled near native complex structures only for one case. The method showed also improved results for the refinement of docked structures in the vicinity of the native binding geometry compared to regular MD refinement.

Improving the performance of the MM/PBSA and MM/GBSA methods in recognizing the native structure of the Bcl-2 family using the interaction entropy method

Correct discrimination of native structure plays an important role in drug design. IE method significantly improves the performance of MM/PB(GB)SA method in discriminating native and decoy structures in protein–ligand/protein systems of Bcl-2 family.

More efficient screening of protein-protein complex model structures for reducing the number of candidates

Rigid-body protein-protein docking is very efficient in generating tens of thousands of docked complex models (decoys) in a very short time without considering structure change upon binding, but typical docking scoring functions are not necessarily sufficiently accurate to narrow these decoys down to a small number of plausible candidates. Flexible refinements and sophisticated evaluation of the decoys are thus required to achieve more accurate prediction. Since this process is time-consuming, an efficient screening method to reduce the number of decoys is necessary immediately following rigid-body dockings. We attempted to develop an efficient screening method by clustering decoys generated by the rigid-body docking ZDOCK. We introduced the three metrics ligand-root-mean-square deviation (L-RMSD), interface-ligand-RMSD (iL-RMSD), and the fraction of common contacts (FCC), and examined various ranges of cut-offs for clusters to determine the best set of clustering parameters. Although the employed clustering algorithm is simple, it successfully reduced the number of decoys. Using iL-RMSD with a cut-off radius of 8 Å, the number of decoys that contain at least one near-native model with 90% probability decreased from 4,808 to 320, a 93% reduction in the original number of decoys. Using FCC for the clustering step, the top 1,000 success rates, defined as the probability that the top 1,000 models contain at least one near-native structure, reached 97%. We conclude that the proposed method is very efficient in selecting a small number of decoys that include near-native decoys.

Refining evERdock: Improved selection of good protein-protein complex models achieved by MD optimization and use of multiple conformations

A method for evaluating binding free energy differences of protein-protein complex structures generated by protein docking was recently developed by some of us. The method, termed evERdock, combined short (2 ns) molecular dynamics (MD) simulations in explicit water and solution theory in the energy representation (ER) and succeeded in selecting the near-native complex structures from a set of decoys. In the current work, we performed longer (up to 100 ns) MD simulations before employing ER analysis in order to further refine the structures of the decoy set with improved binding free energies. Moreover, we estimated the binding free energies for each complex structure based on an average value from five individual MD snapshots. After MD simulations, all decoys exhibit a decrease in binding free energy, suggesting that proper equilibration in explicit solvent resulted in more favourably bound complexes. During the MD simulations, non-native structures tend to become unstable and in some cases dissociate, while near-native structures maintain a stable interface. The energies after the MD simulations show an improved correlation between similarity criteria (such as interface root-mean-square distance) to the native (crystal) structure and the binding free energy. In addition, calculated binding free energies show sensitivity to the number of contacts, which was demonstrated to reflect the relative stability of structures at earlier stages of the MD simulation. We therefore conclude that the additional equilibration step along with the use of multiple conformations can make the evERdock scheme more versatile under low computational cost.